Answer:
[tex]2x+3y=-6[/tex]
Step-by-step explanation:
Let the line is [tex]y=mx+b[/tex] where [tex]m[/tex] is slope and [tex]b[/tex] is [tex]y-intercept[/tex].
The line is parallel to [tex]2x+3y=3[/tex], slope of both the lines will be same.
Find the slope of [tex]2x+3y=3[/tex]
[tex]3y=3-2x\\y=-\frac{2}{3}x+1[/tex]
Slope of line[tex]=-\frac{2}{3}[/tex]
[tex]m=-\frac{2}{3}[/tex]
So the line will be [tex]y=-\frac{2}{3}x+b[/tex]
It passes through [tex](3,-4)[/tex].
[tex]-4=-\frac{2}{3}\times 3+b\\-4=-2+b\\b=-2\\[/tex]
Hence the line is [tex]y=-\frac{2}{3}x-2[/tex]
[tex]y=-\frac{2}{3}x-2\\3y=-2x-6\ \ \ \ \ \ \ (Multiply both sides by 3)\\2x+3y=-6[/tex]
